CHOCOLA  Chocolate
We are given a bar of chocolate composed of m*n square pieces. One should break the chocolate into single squares. Parts of the chocolate may be broken along the vertical and horizontal lines as indicated by the broken lines in the picture.
A single break of a part of the chocolate along a chosen vertical or horizontal line divides that part into two smaller ones. Each break of a part of the chocolate is charged a cost expressed by a positive integer. This cost does not depend on the size of the part that is being broken but only depends on the line the break goes along. Let us denote the costs of breaking along consecutive vertical lines with x_{1}, x_{2}, ..., x_{m1} and along horizontal lines with y_{1}, y_{2}, ..., y_{n1}.
The cost of breaking the whole bar into single squares is the sum of the successive breaks. One should compute the minimal cost of breaking the whole chocolate into single squares.
For example, if we break the chocolate presented in the picture first along the horizontal lines, and next each obtained part along vertical lines then the cost of that breaking will be y_{1}+y_{2}+y_{3}+4*(x_{1}+x_{2}+x_{3}+x_{4}+x_{5}).
Task
Write a program that for each test case:
 Reads the numbers x_{1}, x_{2}, ..., x_{m1} and y_{1}, y_{2}, ..., y_{n1}
 Computes the minimal cost of breaking the whole chocolate into single squares, writes the result.
Input
One integer in the first line, stating the number of test cases, followed by a blank line. There will be not more than 20 tests.
For each test case, at the first line there are two positive integers m and n separated by a single space, 2 <= m,n <= 1000. In the successive m1 lines there are numbers x_{1}, x_{2}, ..., x_{m1}, one per line, 1 <= x_{i} <= 1000. In the successive n1 lines there are numbers y_{1}, y_{2}, ..., y_{n1}, one per line, 1 <= y_{i} <= 1000.
The test cases will be separated by a single blank line.
Output
For each test case : write one integer  the minimal cost of breaking the whole chocolate into single squares.
Example
Input: 1 6 4 2 1 3 1 4 4 1 2 Output: 42
hide comments
subhajit_1999:
20210524 11:52:35
runtime error on python


naman5020:
20210519 15:06:06
Getting NZEC Runtime error in Python 

girsai:
20210312 06:46:53
Greedy First go AC..


mrdevesh_00:
20200626 13:40:57
Can be solved using Greedy!! No dp required 

kushrike:
20200509 22:14:27
Can someone provide a working dp solution 

amansahu112:
20200508 17:17:20
simple greedy.. big first 

mrmajumder:
20200421 08:45:30
dp er chinta baad deo :) 

threat_:
20191015 23:17:14
@gaurav_yadal: look "looking for a challenge" book


gaurav_yadav:
20190802 05:50:09
someone pls tell proof of this greedy approach 

bloodgreed99:
20190313 18:28:17
answer using DP WA

Added by:  ThanhVy Hua 
Date:  20041223 
Time limit:  3s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  10th Polish Olympiad in Informatics, stage 1 